Rectangle

In rectangle ABCD with sides |AB|=19, |AD|=16 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio
∣PB∣∣DP∣\dfrac{ |PB|}{ |DP| }
.

Result

|PB|/|DP| =  1.41

Solution:

∣AB∣2=∣PB∣∣BD∣ ∣AD∣2=∣DP∣∣BD∣  ∣AB∣2∣AD∣2=∣PB∣∣DP∣  ∣PB∣∣DP∣=192162=1.41|AB|^2 = |PB| |BD| \ \\ |AD|^2 = |DP| |BD| \ \\ \ \\ \dfrac{ |AB|^2}{ |AD|^2} = \dfrac{ |PB|}{ |DP| } \ \\ \ \\ \dfrac{ |PB|}{ |DP| } = \dfrac{ 19^2}{ 16^2 } = 1.41

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